Development of New Dimension-Reduction Methods for Reliability, Simulation, and Design of Complex Engineering Systems

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The objective of this research project is to develop new computational methods for uncertainty propagation, reliability analysis, and design optimization of complex engineering systems. The proposed effort will be based on: (1) new dimension-reduction methods for calculating second-moment characteristics of random response; (2) new dimension-reduction and moment-based stochastic methods for reliability analysis; and (3) new algorithms for reliability-based/robust design optimization of structural and mechanical systems. The proposed methods are novel and will be able to address highly nonlinear input-output transformations; unlimited number of random variables or processes; and arbitrarily large uncertainty of input, yet will predict both response moments and reliability accurately. Potential engineering applications include ground vehicle design for durability; fatigue and fracture design of aerospace structures; and design of microelectronics packaging systems. From a fundamental point of view, the dimension-reduction methods will provide an accurate and efficient solution to a general multi-dimensional integral over an arbitrary region. Hence, many problems in basic and applied sciences, which involve uncertainty and/or require evaluation of such integrals, will be solved by the methods developed in this project. The transfer of knowledge created by this project will take place through continued collaboration with industries; organization of symposia on reliability and design in ASME conferences; peer-reviewed journal publications; presentations and publications at major conferences and institutions; and student education. The educational goals comprise recruitment of a female Ph. D. student from underrepresented minority; implementation of software tools from this project in upgrading design and reliability courses; and authoring a comprehensive textbook.